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Chapter 12: Problem 35

A solution is prepared at sea level (external pressure = \(1 \mathrm{~atm}\) ) by dissolving \(100.0 \mathrm{~g}\) of calcium nitrate in \(450.0 \mathrm{~g}\) of water. At what temperature will this solution have a vapor pressure of \(760 \mathrm{~mm} \mathrm{Hg}\) ? (Hint: What does an aqueous solution at sea level do when its vapor pressure is \(760 \mathrm{~mm} \mathrm{Hg}\) ?)

Short Answer

Expert verified
The solution composed of 100 g of calcium nitrate and 450 g of water will have a vapor pressure of 760 mm Hg at \(100.6928^\circ\mathrm{C}\).

Step by step solution

01

1. Consider the relationship between vapor pressure and boiling point

For an aqueous solution at sea level, when its vapor pressure is equal to atmospheric pressure (760 mm Hg), the solution will boil. Therefore, we need to find the boiling point elevation of the given solution in this case.
02

2. Calculate molality (m) of calcium nitrate solution

Calcium nitrate has a molar mass of Ca(NO3)2 = 164.1 g/mol. So, to find the molality (m) of the solution, we first find the number of moles of calcium nitrate: moles of calcium nitrate = mass / molar mass = 100 g / 164.1 g/mol = 0.609 mol Next, we need to find the mass of the solvent (water) in kg: mass of water = 450 g = 0.45 kg Now, we can calculate the molality (m) of the solution: molality (m) = moles of solute / mass of solvent (in kg) = 0.609 mol / 0.45 kg = 1.354 mol/kg
03

3. Calculate boiling point elevation

To determine the boiling point elevation, we use the formula: ΔTb = Kb * m where ΔTb is the boiling point elevation, Kb is the ebullioscopic constant for water (0.512°C/m), and m is the molality of the solution. ΔTb = 0.512°C/m * 1.354 mol/kg = 0.6928°C
04

4. Determine the boiling point of the solution

Since the pure water boils at 100°C, we can now find the boiling point of the solution: Boiling point of solution = boiling point of pure water + boiling point elevation = 100°C + 0.6928°C = 100.6928°C
05

5. Obtain the temperature at which the solution has a vapor pressure of 760 mm Hg

The temperature at which the solution has a vapor pressure of 760 mm Hg is the boiling point of the solution, which we have calculated earlier: Temperature = 100.6928°C So, the solution will have a vapor pressure of 760 mm Hg at 100.6928°C.

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